The Claude plans allow you to send a number of messages to Anthropic models in a specific interval without incurring any extra costs. From Anthropic's "About Claude's Max Plan Usage" page:

> The number of messages you can send per session will vary based on the length of your messages, including the size of files you attach, the length of current conversation, and the model or feature you use. Your session-based usage limit will reset every five hours. If your conversations are relatively short and use a less compute-intensive model, with the Max plan at 5x more usage, you can expect to send at least 225 messages every five hours, and with the Max plan at 20x more usage, at least 900 messages every five hours, often more depending on message length, conversation length, and Claude's current capacity.

So it's not a "Claude Code" subscription, it's a "Claude" subscription.

The only piece of information that might suggest that there are any restrictions to using your subscription to access the models is the part of the Pro plan description that says "Access Claude Code on the web and in your terminal" and the Max plan description that says "Everything in Pro".